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[Each class is different, but here were the last several weeks of a particularly strong class a couple years ago.] Dear Parents, Thursday is our final class. You are welcome to come early, to watch or play with the children. Their final challenge: Build something that doesn’t exist. There has a been a rhythm to the sequence of challenges I have given them. In the past few weeks we’ve had: Building Gulliver — teacher-led, the tallest and most impressive structure we have built Decide what you want to build — it was their call, the opposite of Gulliver. They ended up building a city complete with zoo, runaway dinosaurs, garbage dump, police and ranger station Build the school — our most representational project, in which we began by taking a “field trip” through parts of the school. I built them a miniature of a chair in the classroom, which they thought was very cool. Build an abstract sculpture — or as I said it to the children, “build something that isn’t something and that looks cool.” I first demonstrated two aesthetic criteria, balance and pattern, which many incorporated into their creations. and finally this week, Build something that doesn’t exist — abstract or representational, their choice, but hopefully using balance and pattern. In our initial discussion, I will try to nudge them towards building something together. but that may be beyond them. Most of their work will be without my assistance. They have gotten much better at building together. You may recall that the dragon they built a couple of months ago, judged by their abilities now, was a fiasco.

The story for this week and last has been “The Wolf and the Eight Kid Goats”. Last week I told the story and introduced a math game; this week we acted out the story and continued with our game. Today I asked, “When we come to each new part of the story, if you know a character we’ll need to act our story out, please raise your hand to tell us.” I received all manner of answers. Two girls volunteered to be the door that is locked until mistakenly opened for the Wolf.. The largest boy in class wanted very much to be the littlest baby goat that hides in the grandfather clock and escapes being eaten, and I trust that the role is good and needed for him. Who could know what motivated the boy and girl who wanted to be the bush that the Wolf and the Goats hide behind, but with arms outstretched they made a very noble and chivalrous bush. Some others wanted to be the furniture that gets tossed every which way when the house is invaded by the Wolf, and I was reminded that when The Cat in the Hat was first published, it was deemed scandalously inappropriate for children. Like our story, it has a motif of a house getting wrecked while the mother is away, but there the house-wrecker is the hero, here, the villain. The children take the story very seriously. I was touched watching the mother, who began the story by leaving the house after warning her children. She then waited away from us in silence as events unfolded on the other side of the classroom, as the Wolf tried and tried and finally succeeded in entering the house and then eating the Kid Goats. Only one child wanted the part of the Wolf, but he played it with enthusiasm, and I sensed that was the right part for him that afternoon. Even when we switched from acting to playing our game, no one else would help him make moves for the Wolf, so he played alone vs. all, which he relished. Today’s game was a very simple version of chess, Black Queen (the Wolf) vs. eight White Pawns (the Goats). The Wolf wins if it can gobble up all the Goats. The Goats win if just one of them can advance to the other side of the board and run to their Mother for help. I taught them how the pieces move plus one simple tactic for each side: how to move the Wolf to a square that threatens two Goats at a time — essentially seeing the intersection of lines on the board; and how one Goat can befriend another and protect it. We played, all against the Wolf. When two children initially declared that they didn’t want to play, and I let them sit out, but each was soon drawn into the excitement of the game. All the children advised each other with great enthusiasm on what the best move might be. There were cries of shock and despair each time the Wolf ate up a Goat. One child cried briefly when she couldn’t figure out what would be the best move to do; by that point, the Wolf would eat a Goat no matter what. A couple moves before the end, I asked them to stop and study the game to predict the future, who would win: if each side moved the very best moves it could, who would have to win? They discussed this as they had discussed everything else, and arrived at the correct answer. The children take their story very seriously.

After teaching Building Imagination for three years now, I’ve sorted out four sorts of learnings going on: — Cognitive: This is the mathematical and engineering side of things: how would you design a staircase, how could you make this road ramp up at an angle, can we imagine where the foundation would go before we build it? In the past, we’ve built the Mayflower from simple plan and elevation drawings, we’ve built Gulliver after first imagining what postures were do-able within the constraints of our blocks. Sometimes they figure out a cantilever and we use that in our constructions. I don’t usually verbalize concepts with them, so there may be a lot going on cognitively, but they just think they’re playing. Or as one student said, “This class is really hard but really fun.” — Expressive, therapeutic: The children have strong desires to build particular things. More than once students have vetoed what I thought would be the perfect challenge for them, and I have had no choice but to follow along and lead from behind. Sometimes there is a quality of “playing house” or “playing race cars” in their building. Or happy discoveries, as when last year we built a dragon, and a child jumped over the dragon, but subversively because he presumed it was wrong, but then I invited all to jump over the dragon, as that had been the plan all along. There was something deep and primal in re-enacting this archetype and they kept jumping for a while. I only wish we could have jumped the dragon at night, by a fire. — Artistic: We play with balance, stability, symmetry, representational and non-representational, etc. At the end of class, I often have them look at each others works, “like you were walking in an art museum.” Although they can’t yet articulate why, the children can tell when something is beautiful — there is often a gasp, and then silence, or comments of “That is so cool.” — Social: Sometimes students work well together, sometimes it is a challenge. There are many exercises I use to teach them to cooperate, for example: “Work in pairs and in silence. Take turns, you add one block, then your partner adds one block, then you add a block. Your goal is to make a wall that has a pattern.”

[At Malcolm X, Math Circle is an optional lunchtime activity.] Dear Parents, At 11:39 I was bracing for the onslaught when a tiny girl, a first grader it seemed, came into our hallway on her way to the library. Only she wasn’t going to the library. “I’m here for Math Circle,” she announced to me. She had the quality of a quietly heralding angel. The photos attached are of the first ten minutes and the last 35 minutes. The first ten felt like a 60’s teach-in, full of the sincere, the curious, and those simply seeking to dine out in a new locale, 40+ in all. After a pleasant introduction to topology while they ate lunch, most then chose to go out to the playground, while sixteen chose to go to the library to work on the day’s challenge, figuring out which letters are topologically equivalent. They did this by classifying cut-outs of the letters or by playing a simple drawing game which I named “Morph-It.” The third photograph is two two girls at work playing Morph-It. Notice the second photograph: Math Circle classes usually attract more boys than girls, so it is thrilling to see so many girls here. I can only guess at why. If the alternative is to go out on the playground, perhaps many boys have a greater need than girls for what playground offers. Of the sixteen students, most girls came with one or two friends, but each boy, as far as I could tell, came as an individual. It may be that if girls can approach math with a friend, they are much less frightened or put off than if they face it alone. Lastly, I had prepared two lessons to teach, depending on the crowd, and I chose the one which is geometric rather than numerical, quietly profound rather than splashy and spectacular. That may have spoken more to the girls, or at least to a certain personality type.Whatever the reason for so many girls, that seems something precious that we should hold on to. As well, it was wonderful to meet several students whom I had not met before. There were several students whom I was expecting, but I am sorry did not show up, and others who stayed for the initial talk but chose not to continue the math challenge in the library. I saw one boy after school who had forgotten to come, and he felt bad for having missed it. It may take a couple of weeks, but we’ll get the kinks out. Topologically speaking, there are only nine distinct shapes that make up the letters of our alphabet. I heard afterwards from Mr. Hunt [the principal] that some students had come up to challenge him, how many letters are there in the alphabet? Then they explained to him that there are 9, not 26. Henri